How do you simplify #[2x(x+6)^4x^2(4)(x+6)^3]/(x+6)^8#?
Expression
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To simplify the expression [2x(x+6)^4x^2(4)(x+6)^3]/(x+6)^8, you can follow these steps:

Expand the terms inside the brackets: [2x(x^4 + 4x^3(6) + 6^2x^2(4) + 6^3x(4) + 6^4)  x^2(4)(x^3 + 3x^2(6) + 3^2x(6^2) + 6^3)] / (x+6)^8

Simplify the expanded expression: [2x^5 + 48x^4 + 288x^3 + 1152x^2 + 20736x  4x^6  72x^5  432x^4  1728x^3] / (x+6)^8

Combine like terms: (2x^6  24x^5  144x^4 + 288x^3 + 1152x^2 + 20736x) / (x+6)^8
Therefore, the simplified expression is (2x^6  24x^5  144x^4 + 288x^3 + 1152x^2 + 20736x) / (x+6)^8.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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